Biharmonic Maps from Tori into a 2-Sphere |
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Authors: | Zeping WANG Ye-Lin OU and Hanchun YANG |
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Institution: | 1.Department of Mathematics,Yunnan University,Kunming,China;2.Department of Mathematics,Guizhou Normal University,Guiyang,China;3.Department of Mathematics,Texas A & M University-Commerce,Commerce,USA |
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Abstract: | Biharmonic maps are generalizations of harmonic maps. A well-known result on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere (whatever the metrics chosen) in the homotopy class of maps of Brower degree ±1. It would be interesting to know if there exists any biharmonic map in that homotopy class of maps. The authors obtain some classifications on biharmonic maps from a torus into a sphere, where the torus is provided with a flat or a class of non-flat metrics whilst the sphere is provided with the standard metric. The results in this paper show that there exists no proper biharmonic maps of degree ±1 in a large family of maps from a torus into a sphere. |
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Keywords: | Biharmonic maps Biharmonic tori Harmonic maps Gauss maps Maps into a sphere |
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